We consider a continuous-time and infinite-horizon version of the setting of [1]}.
We postulate a trader who wants to liquidate \(x \in \mathbb {X}\)  units of an asset over an
infinite-time horizon.The choice of an infinite-horizon setting is
important since as it will allow an analytical solution of the problem. In particular, in an
infinite-horizon setting, the optimal policy is stationary over time, and hence time can be
eliminated as a state variable. As we will see in subsequent sections, this results in a
simpler Hamilton-Jacobi-Bellman (HJB) equation that can be solved analytically. Beyond this,
in some sense the infinite-horizon setting is more elegant from a modeling perspective since
it endogenizes the effective time horizon of the trader dynamically as a function of risk
aversion. That said, the optimal policy for a finite-horizon variation of our setting could
be obtained via a numerical solution of the HJB equation, and we expect the qualitative
insights to be no different. Here, \(x\)  can be negative if the trader wants to acquire the
asset. We define \(\mathbb {X} \triangleq [-M, M] \subset \mathbb {R}\) , where \(M \ge 0\)  is an arbitrary
large numberWe require that the position size be bounded in order to resolve technical
difficulties (see Remark REF ). that represents the largest possible position size
that the trader is allowed to own.
